License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2020.97
URN: urn:nbn:de:0030-drops-125042
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12504/
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Shimizu, Nobutaka ; Shiraga, Takeharu

Quasi-Majority Functional Voting on Expander Graphs

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LIPIcs-ICALP-2020-97.pdf (0.6 MB)

Abstract

Consider a distributed graph where each vertex holds one of two distinct opinions. In this paper, we are interested in synchronous voting processes where each vertex updates its opinion according to a predefined common local updating rule. For example, each vertex adopts the majority opinion among 1) itself and two randomly picked neighbors in best-of-two or 2) three randomly picked neighbors in best-of-three. Previous works intensively studied specific rules including best-of-two and best-of-three individually.
In this paper, we generalize and extend previous works of best-of-two and best-of-three on expander graphs by proposing a new model, quasi-majority functional voting. This new model contains best-of-two and best-of-three as special cases. We show that, on expander graphs with sufficiently large initial bias, any quasi-majority functional voting reaches consensus within O(log n) steps with high probability. Moreover, we show that, for any initial opinion configuration, any quasi-majority functional voting on expander graphs with higher expansion (e.g., Erdős-Rényi graph G(n,p) with p = Ω(1/√n)) reaches consensus within O(log n) with high probability. Furthermore, we show that the consensus time is O(log n/log k) of best-of-(2k+1) for k = o(n/log n).

BibTeX - Entry

@InProceedings{shimizu_et_al:LIPIcs:2020:12504,
  author =	{Nobutaka Shimizu and Takeharu Shiraga},
  title =	{{Quasi-Majority Functional Voting on Expander Graphs}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{97:1--97:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Artur Czumaj and Anuj Dawar and Emanuela Merelli},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12504},
  URN =		{urn:nbn:de:0030-drops-125042},
  doi =		{10.4230/LIPIcs.ICALP.2020.97},
  annote =	{Keywords: Distributed voting, consensus problem, expander graph, Markov chain}
}

Keywords: Distributed voting, consensus problem, expander graph, Markov chain
Collection: 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)
Issue Date: 2020
Date of publication: 29.06.2020

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